Simplify the following expression: $ x = \dfrac{-5}{3} - \dfrac{p}{4p - 10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4p - 10}{4p - 10}$ $ \dfrac{-5}{3} \times \dfrac{4p - 10}{4p - 10} = \dfrac{-20p + 50}{12p - 30} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{p}{4p - 10} \times \dfrac{3}{3} = \dfrac{3p}{12p - 30} $ Therefore $ x = \dfrac{-20p + 50}{12p - 30} - \dfrac{3p}{12p - 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-20p + 50 - 3p }{12p - 30} $ Distribute the negative sign: $x = \dfrac{-20p + 50 - 3p}{12p - 30}$ $x = \dfrac{-23p + 50}{12p - 30}$